Who owns an option?

When you sell a call does it go to a specific buyer (only one person who owns the call you sold) or can anyone who has bought an option on that stock exercise it? Hope you can understand what I am trying to say. TIA

A specific buyer purchases the call that you sell. However, anyone owning that same call can exercise it and you could be the one assigned. OCC assignment to the broker is random but I think brokers may have specific rules as to how they dole out assignments.

Let's say you offer a call at 1.00, and Joe Blow buys it. Your contract now is not with Joe, it is with the Options Clearing Corporation. Joe's contract is also with the Options Clearing Corporation. So if you go bankrupt and can't meet your obligation to sell Joe stock at the strike price, Joe's option is still good. That's the function of the OCC - to guarantee every trade by standing between the two parties and assuming the obligation for that option to perform.

If at some point Joe decides to exercise his option, the OCC will assign it to somebody who is short that option, but not necessarily to you.

Lets say I sell a call for $2.00, the stock tanks from $30 to $20 and that option is now .50, then the stock comes back to $31. The first buyer is at a loss, but could the second buyer exercise my sell for a profit? Or does it have to be someone who paid the 2.00 to call my stock? Just wondering when I would know if I am in the clear and don't have to worry about being called. TIA

An option is the right to buy (call) or sell (put) a specific underlying.

The seller of the option has the obligation to fulfill the terms of the contract. It doesn't matter who bought it when or at what price or how many times it has changed hands or whether they made or lost money on their position. You are short that contract. If your short call is assigned, you must deliver the stock or carry a short stock position.

Let's say you offer a call at 1.00, and Joe Blow buys it. Your contract now is not with Joe, it is with the Options Clearing Corporation. Joe's contract is also with the Options Clearing Corporation. So if you go bankrupt and can't meet your obligation to sell Joe stock at the strike price, Joe's option is still good. That's the function of the OCC - to guarantee every trade by standing between the two parties and assuming the obligation for that option to perform.

If at some point Joe decides to exercise his option, the OCC will assign it to somebody who is short that option, but not necessarily to you.